Fast Optimal Design of Semiconductor Devices

This paper presents a new approach to the design of semiconductor devices, which leads to fast optimization methods whose numerical effort is of the same order as a single forward simulation of the underlying model, the stationary drift-diffusion system. The design goal we investigate is to increase the outflow current on a contact for fixed applied voltage; the natural design variable is the doping profile. By reinterpreting the doping profile as a state variable and the electrostatic potential as the new design variable, we obtain a simpler optimization problem, whose Karush--Kuhn--Tucker conditions partially decouple. This property allows us to construct efficient iterative optimization algorithms, which avoid solving the fully coupled drift-diffusion system, and need only solves of the continuity equations and their adjoints. The efficiency and success of the new approach is demonstrated in several numerical examples.